1. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 1 Biomedical Imaging I Class 5 – Radionuclide Imaging (PET, SPECT), Part 3: Attenuation and Scatter Corrections 10/12/05

2. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 2 Recommended Reading K. Miles, P. Dawson, and M. Blomley (Eds.), Functional Computed Tomography (Isis Medical Media, Oxford, 1997). R. J. English, SPECT: Single Photon Emission Computed Tomography: A Primer (Society of Nuclear Medicine, Reston, VA, 1995). M. Reivich and A. Alavi (Eds.), Positron Emission Tomography (A. R. Liss, NY, 1985).

3. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 3 Characteristics of SPECT & PET images Low spatial resolution Dose limitations → long acquisition time Imperfect tissue selectivity Scatter effects Low SNR Dose limitations → poor counting statistics Attenuation High CNR Essentially no signal except from the administered radionuclide Post-processing operations improve SNR at the expense of spatial resolution Spatial low pass (“long pass”) filtering

4. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 4 Interplay of spatial resolution and CNR Ideal case: – No “bleeding” of signal from one location into the adjacent ones – Difference between signal arising from adjacent positions determines the contrast, and hence the CNR Reality: – Lateral spreading of image information results in lowering of high signal levels and raising of low ones – The apparent signal difference between adjacent sites is lower than in the ideal case, and so the CNR is lower

5. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 5 Attenuation Correction

6. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 6 Projection Operator f(x,y)f(x,y) x θ x s y -a a

7. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 7 Projection Operator — CT vs. ECT x–ray CT: ECT: spatial distribution of attenuation coefficient spatial distribution of radioactivity

8. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 8 X-Ray Energy & Contrast 20 keV 200 keV 2000 keV (= 2MeV) 99m Tc γ -ray photons e - -e + annihilation γ -ray photons

9. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 9 Other approaches to attenuation correction Use co-registered anatomical image (e.g., MRI, x-ray CT) to generate an estimate of the tissue µ at each location, and insert that into Eq. (2) (Slide 7) Use known-strength γ -emitting standards (e.g., 153 Gd (Webb, §2.9.2, p. 79) or 68 Ge (§ 2.11.4.1, p. 95)) in conjunction with image data collection, to estimate µ at each tissue location Iterative image reconstruction algorithms In “odd-numbered” iterations, treat µ(u,v) as known and fixed, and solve for ρ(x,y) In “even-numbered” iterations, treat ρ(x,y) as known and fixed, and solve for µ(u,v) Even more elaborate mathematical techniques, e.g., E. Y. Sidky and X. Pan, “Image reconstruction with a half–detector in single–photon emission computed tomography with nonuniform attenuation,” Optical Engineering 42(9), 2506-2513 (2003). I. Laurette et al., “A three–dimensional ray–driven attenuation, scatter and geometric response correction technique for SPECT in inhomogeneous media,” Physics in Medicine and Biology 45, 3459-3480 (2000). T. Kauppinen et al., “Improvement of brain perfusion SPET using iterative reconstruction with scatter and non–uniform attenuation correction,” European J. Nuclear Medicine 27(9), 1380-1386 (2000).

10. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 10 Scatter Correction

11. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 11 Origins of scatter artifacts Accidental coincidences (PET) Compton scatter events (SPECT and PET) Can redirect photons within measurement plane, or can redirect photons arising from outside measurement plane into it (assuming ring-shaped detector array) Spatially and directionally distributed source Higher photon energy than in x-ray CT means that detector collimation is less effective More serious problem for area detectors (for whole-body imaging, for example) than for ring-shaped detector arrays

12. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 12 Inherent Dimensionality

13. BMI I FS05 – Class 4 “Nuclear Imaging: Math” Slide 13 Scatter correction techniques Compton scattering (SPECT & PET) Energy “sub-window” method (Webb, §2.9.2, p. 78) Extrapolation of scattered “source” strength, from image regions outside the patient’s body, to image regions within it (§2.11.4.2, p. 97) Accidental coincidences (PET) True but impractical: if the radius r of the detector ring is varied, the rate of true coincidences is proportional to 1/r, while the accidental coincidence rate is proportional to 1/r 2 Accidental coincidence rate for a pair of detector is proportional to the product of the overall count rates for each By increasing the delay between the timing pulses sent to each detector in a pair, can selectively detect only accidental coincidences